FWIW, upgrading to 9.5.rc4 *and disabling the use of system’s pari and
singular* gives the same symptoms. Possible suspect :
charpent@zen-book-flip:~$ sage -pip list | grep pari
cypari2 2.1.2
I’m way out of my depth here…
HTH,
Le samedi 29 janvier 2022 à 22:51:14 UTC+1, Emmanuel Charpentier a écrit :
> The promlem seems tolie wit (my use of) polynomial rings to compute the
> eigenvectors. Manually, after executing
>
> dims = M.dimensions()
> if dims[0] != dims[1]: raise DomainError("Not a square matrix !")
> dim = dims[0]
> BR = M.base_ring()
> try:
> WR = BR.algebraic_closure()
> except AttributeError:
> WR = BR
> WPR = WR["t"]
> t = WPR.gens()[0]
> # CP = WPR(M.charpoly(var="t"))
> # Eigenvalues
> CP = M.charpoly(var="t")
> lambdas = CP.roots(ring=WR)
> # Eigenvectors
> Id = identity_matrix(WR,dim)
> WM = M.apply_map(lambda u:WR(u))
> PR = PolynomialRing(WR,list(("v%d"%u for u in range(dim))))
> J=PR.ideal(*(WM-Id*lambdas[0][0])*vector(PR.gens()))
>
> neither J.dimension() nor J.variety() returns ; the interruption gives :
>
> sage: J.dimension()
> C-c
> C-c---------------------------------------------------------------------------
> KeyboardInterrupt Traceback (most recent call last)
> <ipython-input-684-2e62bddf16b7> in <module>
> ----> 1 J.dimension()
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
> in __call__(self, *args, **kwds)
> 295 if not R.base_ring().is_field():
> 296 raise ValueError("Coefficient ring must be a field for
> function '%s'."%(self.f.__name__))
> --> 297 return self.f(self._instance, *args, **kwds)
> 298
> 299 require_field = RequireField
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar_decorators.py
> in wrapper(*args, **kwds)
> 111 # same_field=True might trigger an exception otherwise.
> 112
> --> 113 numfield, new_elems, morphism =
> number_field_elements_from_algebraics(orig_elems, same_field=True,
> minimal=True)
> 114
> 115 elem_dict = dict(zip(orig_elems, new_elems))
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in number_field_elements_from_algebraics(numbers, minimal, same_field,
> embedded, prec)
> 2759 real_numbers = []
> 2760 for v in numbers:
> -> 2761 if v._exact_field().is_complex() and real_case:
> 2762 # the number comes from a complex algebraic number field
> 2763 embedded_rt = v.interval_fast(RealIntervalField(prec))
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in _exact_field(self)
> 4428 if isinstance(sd, (ANRational, ANExtensionElement)):
> 4429 return sd.generator()
> -> 4430 self.exactify()
> 4431 return self._exact_field()
> 4432
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
> 4364 return
> -> 4365 self._set_descr(self._descr.exactify())
> 4366
> 4367 def _set_descr(self, new_descr):
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 8180
> 8181 if op == 'real':
> -> 8182 arg.exactify()
> 8183 rv = (arg + arg.conjugate()) / 2
> 8184 rv.exactify()
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
> 4364 return
> -> 4365 self._set_descr(self._descr.exactify())
> 4366
> 4367 def _set_descr(self, new_descr):
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 8429 left = self._left
> 8430 right = self._right
> -> 8431 left.exactify()
> 8432 right.exactify()
> 8433 gen = left._exact_field().union(right._exact_field())
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
> 4364 return
> -> 4365 self._set_descr(self._descr.exactify())
> 4366
> 4367 def _set_descr(self, new_descr):
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in exactify(self)
> 8431 left.exactify()
> 8432 right.exactify()
> -> 8433 gen = left._exact_field().union(right._exact_field())
> 8434 left_value = gen(left._exact_value())
> 8435 right_value = gen(right._exact_value())
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in union(self, other)
> 3230 op = QQx(op)
> 3231 # pari_nf = self._field.pari_nf()
> -> 3232 pari_nf = self.pari_field()
> 3233 factors = list(pari_nf.nffactor(op).lift())[0]
> 3234 x, y = QQxy.gens()
>
> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
> in pari_field(self)
> 3134 if self._pari_field is None:
> 3135 pari_pol = self._field.pari_polynomial("y")
> -> 3136 self._pari_field = pari_pol.nfinit(1)
> 3137 return self._pari_field
> 3138
>
> cypari2/auto_gen.pxi in cypari2.gen.Gen_base.nfinit()
>
> KeyboardInterrupt:
>
> Suggestions ?
>
> Le samedi 29 janvier 2022 à 15:34:05 UTC+1, Emmanuel Charpentier a écrit :
>
>> Setup : Sage 9.5.rc1 running in Debian testing on core i7 + 16 GB RAM.
>>
>> def test(Size=2, Ring=QQ):
>> from time import time as stime
>> with seed(0):
>> M = matrix(Ring, Size, Size, lambda u, v:Ring.random_element())
>> t0 = stime()
>> SL = M.eigenspaces_left(algebraic_multiplicity=True)
>> t1 = stime()
>> VL = M.eigenvectors_left()
>> t2 = stime()
>> return t1-t0, SL, t2-t1, VL
>>
>> test() runs as expected, as well as test(Size=5) and test(Ring=AA), with
>> very reasonable runtimes (under a second, IIRC). But test(Size=3,
>> Ring=AA) “never returns” (meaning that it hadn’t returned when I
>> interrupted it after tens of minutes). Further exploration showec that
>> neither M.eigenspaces_left(algebraic_multiplicity=True) nor
>> M.eigenvectors_left() return.
>>
>> Is that an expected behaviour ?
>>
>> FWIW, stack trace at interruption :
>>
>> sage: AA3=test(Size=3, Ring=AA)
>> AA3=test(Size=3, Ring=AA) C-c
>> C-c---------------------------------------------------------------------------
>> AttributeError Traceback (most recent call last)
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in minpoly(self)
>> 4492 try:
>> -> 4493 return self._minimal_polynomial
>> 4494 except AttributeError:
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/structure/element.pyx
>> in sage.structure.element.Element.__getattr__
>> (build/cythonized/sage/structure/element.c:4754)()
>> 493 """
>> --> 494 return self.getattr_from_category(name)
>> 495
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/structure/element.pyx
>> in sage.structure.element.Element.getattr_from_category
>> (build/cythonized/sage/structure/element.c:4866)()
>> 506 cls = P._abstract_element_class
>> --> 507 return getattr_from_other_class(self, cls, name)
>> 508
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/cpython/getattr.pyx
>> in sage.cpython.getattr.getattr_from_other_class
>> (build/cythonized/sage/cpython/getattr.c:2633)()
>> 360 dummy_error_message.name = name
>> --> 361 raise AttributeError(dummy_error_message)
>> 362 attribute = <object>attr
>>
>> AttributeError: 'sage.rings.real_mpfi.RealIntervalFieldElement' object has
>> no attribute '_evaluate_polynomial'
>>
>> During handling of the above exception, another exception occurred:
>>
>> KeyboardInterrupt Traceback (most recent call last)
>> <ipython-input-344-ff7c46010ad2> in <module>
>> ----> 1 AA3=test(Size=Integer(3), Ring=AA)
>>
>> <string> in test(Size, Ring)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.eigenspaces_left
>> (build/cythonized/sage/matrix/matrix2.c:43588)()
>> 6270 self = self.change_ring(F)
>> 6271 A = self - alpha
>> -> 6272 W = A.kernel()
>> 6273 V.append((alpha,
>> W.ambient_module().span_of_basis(W.basis()), e))
>> 6274 else:
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.left_kernel
>> (build/cythonized/sage/matrix/matrix2.c:32440)()
>> 4947
>> 4948 tm = verbose("computing left kernel for %sx%s matrix" %
>> (self.nrows(), self.ncols()),level=1)
>> -> 4949 K = self.transpose().right_kernel(*args, **kwds)
>> 4950 self.cache('left_kernel', K)
>> 4951 verbose("done computing left kernel for %sx%s matrix" %
>> (self.nrows(), self.ncols()),level=1,t=tm)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.right_kernel
>> (build/cythonized/sage/matrix/matrix2.c:31909)()
>> 4785
>> 4786 # Go get the kernel matrix, this is where it all happens
>> -> 4787 M = self.right_kernel_matrix(*args, **kwds)
>> 4788
>> 4789 ambient = R**self.ncols()
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.right_kernel_matrix
>> (build/cythonized/sage/matrix/matrix2.c:30829)()
>> 4394
>> 4395 if M is None and R in _Fields:
>> -> 4396 format, M = self._right_kernel_matrix_over_field()
>> 4397
>> 4398 if M is None and R.is_integral_domain():
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix._right_kernel_matrix_over_field
>> (build/cythonized/sage/matrix/matrix2.c:27969)()
>> 3686 from sage.matrix.matrix_space import MatrixSpace
>> 3687 tm = verbose("computing right kernel matrix over an
>> arbitrary field for %sx%s matrix" % (self.nrows(), self.ncols()),level=1)
>> -> 3688 E = self.echelon_form(*args, **kwds)
>> 3689 pivots = E.pivots()
>> 3690 pivots_set = set(pivots)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.echelon_form
>> (build/cythonized/sage/matrix/matrix2.c:52440)()
>> 7686 E = self.__copy__()
>> 7687 if algorithm == 'default':
>> -> 7688 v = E.echelonize(cutoff=cutoff, **kwds)
>> 7689 else:
>> 7690 v = E.echelonize(algorithm = algorithm, cutoff=cutoff,
>> **kwds)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix.echelonize
>> (build/cythonized/sage/matrix/matrix2.c:51817)()
>> 7583 if self.base_ring() in _Fields:
>> 7584 if algorithm in ['classical', 'partial_pivoting',
>> 'scaled_partial_pivoting', 'scaled_partial_pivoting_valuation']:
>> -> 7585 self._echelon_in_place(algorithm)
>> 7586 elif algorithm == 'strassen':
>> 7587 self._echelon_strassen(cutoff)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/matrix/matrix2.pyx
>> in sage.matrix.matrix2.Matrix._echelon_in_place
>> (build/cythonized/sage/matrix/matrix2.c:53308)()
>> 7848 sig_check()
>> 7849 for r in range(start_row, nr):
>> -> 7850 if A.get_unsafe(r, c):
>> 7851 pivots.append(c)
>> 7852 a_inverse = ~A.get_unsafe(r, c)
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in __bool__(self)
>> 4043 right = sd._right if op is operator.sub else -sd._right
>> 4044
>> -> 4045 lp = left.minpoly()
>> 4046 rp = right.minpoly()
>> 4047 if lp != rp:
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in minpoly(self)
>> 4493 return self._minimal_polynomial
>> 4494 except AttributeError:
>> -> 4495 self.exactify()
>> 4496 self._minimal_polynomial = self._descr.minpoly()
>> 4497 return self._minimal_polynomial
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
>> 4364 return
>> -> 4365 self._set_descr(self._descr.exactify())
>> 4366
>> 4367 def _set_descr(self, new_descr):
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 8430 right = self._right
>> 8431 left.exactify()
>> -> 8432 right.exactify()
>> 8433 gen = left._exact_field().union(right._exact_field())
>> 8434 left_value = gen(left._exact_value())
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
>> 4364 return
>> -> 4365 self._set_descr(self._descr.exactify())
>> 4366
>> 4367 def _set_descr(self, new_descr):
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 8430 right = self._right
>> 8431 left.exactify()
>> -> 8432 right.exactify()
>> 8433 gen = left._exact_field().union(right._exact_field())
>> 8434 left_value = gen(left._exact_value())
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
>> 4364 return
>> -> 4365 self._set_descr(self._descr.exactify())
>> 4366
>> 4367 def _set_descr(self, new_descr):
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 8430 right = self._right
>> 8431 left.exactify()
>> -> 8432 right.exactify()
>> 8433 gen = left._exact_field().union(right._exact_field())
>> 8434 left_value = gen(left._exact_value())
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
>> 4364 return
>> -> 4365 self._set_descr(self._descr.exactify())
>> 4366
>> 4367 def _set_descr(self, new_descr):
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 8176
>> 8177 if op == '~':
>> -> 8178 arg.exactify()
>> 8179 return arg._descr.invert(None)
>> 8180
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 4363 if isinstance(od, (ANRational, ANExtensionElement)):
>> 4364 return
>> -> 4365 self._set_descr(self._descr.exactify())
>> 4366
>> 4367 def _set_descr(self, new_descr):
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in exactify(self)
>> 8431 left.exactify()
>> 8432 right.exactify()
>> -> 8433 gen = left._exact_field().union(right._exact_field())
>> 8434 left_value = gen(left._exact_value())
>> 8435 right_value = gen(right._exact_value())
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in union(self, other)
>> 3230 op = QQx(op)
>> 3231 # pari_nf = self._field.pari_nf()
>> -> 3232 pari_nf = self.pari_field()
>> 3233 factors = list(pari_nf.nffactor(op).lift())[0]
>> 3234 x, y = QQxy.gens()
>>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>> in pari_field(self)
>> 3134 if self._pari_field is None:
>> 3135 pari_pol = self._field.pari_polynomial("y")
>> -> 3136 self._pari_field = pari_pol.nfinit(1)
>> 3137 return self._pari_field
>> 3138
>>
>> cypari2/auto_gen.pxi in cypari2.gen.Gen_base.nfinit()
>> KeyboardInterrupt:
>>
>> Any hint appreciated…
>>
>>
>
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